The use of genetic variants as instrumental variables – an approach known as Mendelian randomization – is a popular epidemiological method for estimating the causal effect of an exposure (phenotype, biomarker, risk factor) on a disease or health-related outcome from observational data. Instrumental variables must satisfy strong, often untestable assumptions, which means that finding good genetic instruments among a large list of potential candidates is challenging. This difficulty is compounded by the fact that many genetic variants influence more than one phenotype through different causal pathways, a phenomenon called horizontal pleiotropy. This leads to errors not only in estimating the magnitude of the causal effect, but also in inferring the direction of the putative causal link. We propose a Bayesian approach (BayesMR) that is a generalization of the Mendelian randomization technique in which we allow for pleiotropic effects and, crucially, for the possibility of reverse causation. The output of the method is a posterior distribution over the target causal effect, which provides an immediate and easily interpretable measure of the uncertainty in the estimation. More importantly, with the BayesMR algorithm we can estimate the model evidence for both directions to determine how much more likely the expected direction is relative to the reverse direction.

The data set contains source code implementing the BayesMR algorithm, which is described in the article titled "Inferring the Direction of a Causal Link and Estimating Its Effect via a Bayesian Mendelian Randomization Approach"(https://doi.org/10.1177/0962280219851817) by Ioan Gabriel Bucur, Tom Claassen and Tom Heskes. The data set also contains simulated data necessary for exactly reproducing the figures in the article as well as the routines necessary for recreating it. This research is presented in Chapter 4 of the PhD thesis titled "Being Bayesian about Causal Inference" by Ioan Gabriel Bucur. The code is written in the R and C++ programming languages.